Barletti, Luigi and Cintolesi, Carlo (2012) Derivation of isothermal quantum fluid equations with Fermi-Dirac and Bose-Einstein statistics. Technical Report (2012.03.29, no. 1), Dipartimento di Matematica "U.Dini", Universita' di Firenze.

Abstract

By using the quantum maximum entropy principle we formally derive, from a underlying kinetic description, isothermal (hydrodynamic and diffusive) quantum fluid equations for particles with Fermi-Dirac and Bose-Einstein statistics. A semiclassical expansion of the quantum fluid equations, up to O(h^2)-terms, leads to classical fluid equations with statistics-dependent quantum corrections, including a modified Bohm potential. The Maxwell-Boltzmann limit and the zero temperature limit are eventually discussed.